On the Construction and the Structure of Off-Shell Supermultiplet Quotients

TL;DR

This paper introduces a method to construct and analyze complex supermultiplets in supersymmetry by using gauge-quotients of Adinkras, leading to an infinite sequence of larger supermultiplets, expanding the classification of supersymmetric representations.

Contribution

It presents a novel gauge-quotient construction that generates new supermultiplets beyond Adinkras, forming connected networks and creating an infinite hierarchy of representations.

Findings

Supermultiplets can be constructed as gauge-quotients of Adinkras.

The resulting supermultiplets form connected networks of Adinkras.

An infinite sequence of larger supermultiplets is generated, analogous to Weyl's construction.

Abstract

Recent efforts to classify representations of supersymmetry with no central charge have focused on supermultiplets that are aptly depicted by Adinkras, wherein every supersymmetry generator transforms each component field into precisely one other component field or its derivative. Herein, we study gauge-quotients of direct sums of Adinkras by a supersymmetric image of another Adinkra and thus solve a puzzle from Ref.[2]: The so-defined supermultiplets do not produce Adinkras but more general types of supermultiplets, each depicted as a connected network of Adinkras. Iterating this gauge-quotient construction then yields an indefinite sequence of ever larger supermultiplets, reminiscent of Weyl's construction that is known to produce all finite-dimensional unitary representations in Lie algebras.